Abstract
A unified variational framework and finite element simulations of phase transformation dynamics in shape memory alloy thin films are reported in this paper. The computational model is based on an approach which combines the lattice based kinetics involving the order variables and non-equilibrium thermodynamics. Algorithmic and computational issues are discussed. Numerical results on phase nucleation under mechanical loading are reported.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Ball, J.M., Carstensen, C.: Compatibility conditions for microstructures and the austenite-martensite transition. Mater. Sci. and Eng. A 273, 231–236 (1999)
Bhattacharya, K.: Microstructure of Martensite. Oxford University Press, Oxford (2003)
Belik, P., Luskin, M.: Computational modeling of softening in a structural phase transformation. Multiscale Model. Simul. 3(4), 764–781 (2005)
Abeyaratne, R., Chu, C., James, R.D.: Kinetics of materials with wiggly energies: The evolution of twinning microstructure in a Cu-Al-Ni shape memory alloys. Phil. Mag. 73A, 457–496 (1996)
Artemev, A., Wang, Y., Khachaturyan, A.G.: Three-dimensional phase field model and simulation of martensitic transformation in multilayer systems under applied stresses. Acta Mater. 48, 2503–2518 (2000)
Ichitsubo, T., Tanaka, K., Koiwa, M., Yamazaki, Y.: Kinetics of cubic to tetragonal transformation under external field by the time-dependent Ginzburg-Landau approach. Phy. Rev. B 62, 5435 (2000)
Auricchio, F., Petrini, L.: A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems. Int. J. Numer. Meth. Engng. 61, 807–836 (2004)
Levitas, V.I., Preston, D.L.: Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite \(\leftrightarrow\) martensite. Phys. Rev. B 66, 134–206 (2002)
Levitas, V.I., Preston, D.L., Lee, D.W.: Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. III. Alternative potentials, critical nuclei, kink solutions, and dislocation theory. Phys. Rev. B 68, 134–201 (2003)
Mahapatra, D.R., Melnik, R.V.N.: A dynamic model for phase transformations in 3D samples of shape memory alloys. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2005. LNCS, vol. 3516, pp. 25–32. Springer, Heidelberg (2005)
Roy Mahapatra, D., Melnik, R.V.N.: Finite element approach to modelling evolution of 3D shape memory materials, Math. Computers Simul (September 2005) (submitted)
Falk, F., Kanopka, P.: Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys. J. Phys.: Condens. Matter 2, 61–77 (1990)
Boyd, J.G., Lagoudas, D.C.: A thermodynamical constitutive constitutive model for shape memory materials. Part I. the monolithic shape memory alloy. Int. J. Plasticity 12(6), 805–842 (1996)
Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Springer, Heidelberg (1997)
Boullay, P., Schryvers, D., Ball, J.M.: Nanostructures at martensite macrotwin interfaces in Ni65Al35. Acta Mater. 51, 1421–1436 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mahapatra, D.R., Melnik, R.V.N. (2006). Numerical Simulation of Phase Transformations in Shape Memory Alloy Thin Films. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758525_16
Download citation
DOI: https://doi.org/10.1007/11758525_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34381-3
Online ISBN: 978-3-540-34382-0
eBook Packages: Computer ScienceComputer Science (R0)